Apparatus for damping axial coherent beam instabilities in a synchrotron particle accelerator



April 16, 1968 Filed Sept. 7,

R. H. HILDEN ET APPARATUS FOR DAMPING AXIAIJ COHERENT BEAM INSTABILITIES IN A SYNCHROTRON PARTICLE ACCELERATOR 1966 SOURCE 0F 4 Sheets-Sheet 1.

5 14 10 zivmay SOURCE INS/DE KONcHEs) ours/DE April 16, 1968 R, H|LDEN ET AL 3,378,778

APPARATUS FOR DAMPING AXIAL COHERENT BEAM INSTABILITIES IN A SYNCHROTRON PARTICLE ACCELERATOR Filed Sept. 7, 1966 4 Sheets-Sheet 1.

REE Prmss April 16, 1968 R. H. HILDEN ET AL APPARATUS FOR DAMPING AXIAL COHERENT BEAM INSTABILITIES IN A SYNCHROTRON PARTICLE ACCELERATOR Filed Sept. 7, 1966 4 Sheets-Sheet 3 United States Patent Oflice Patented Apr. 16, 1968 3,378,778 APPARATUS FOR DAMPIN G AXIAL COHERENT BEAM INSTABILITIES IN A SYNCHROTRON PARTIQLE ACCELERATOR Richard H. Hildcn, Minneapolis, Minn., John H. Martin,

Lisle, Iil., Frederick E. Mills, Madison, Wis., and Russell A. Winje, Naperville, Ill., assignors to the United States of America as represented by the United States Atomic Energy Commission Filed Sept. 7, 1966, Ser. No. 577,782 3 Claims. (Cl. 328-235) The invention described herein was made in the course of, or under, a contract with the United States Atomic Energy Commission.

This invention relates to synchrotron particle accelerators and more particularly to a method of and apparatus for damping axial, coherent beam instabilities in a synchrotron particle accelerator.

A synchrotron particle accelerator is one in which groups or bunches of charged particles are accelerated to high energies in a fixed, circular, closed orbit by the repetitive application of radio frequency (RF) energy. The bunches are contained in a fixed orbit by a magnetic field imposed perpendicular to the fixed orbit; and relative motion of a bunch is referred to as being axial if the motion is in the direction of the magnetic field, or radial if the motion is transverse of the bending magnetic field. The radio frequency energy source has a continuously increasing frequency to compensate for increases in velocity of the bunches; and the magnetic field must continuously increase in intensity in a predetermined relationship with the frequency increases of the RF energy source to contain the bunches in a fixed orbit.

Particles under-going acceleration are subject to a variety of forces which cause them to stray from the ideal orbit. Consequently, means must be provided to deflect particles back into the ideal orbit. The oscillations which thereby result are called betatron oscillations for historical reasons. These betatron oscillations are in the directions transverse to the direction of the particle beam and can be characterized as axial or radial. One possible mode of betatron oscillation is that in which all the particles in a beam bunch move in the same phase. Such an oscillation is called a coherent betatron oscillation. It has been found that forces arising from currents and charges induced on the walls of the vacuum chamber surrounding the beam, or forces arising from trapped ions in the beam, can cause these coherent oscillations to be unstable in the sense that their amplitude increases with time. Whether the axial or radial mode of coherent betatron oscillation is unstable depends primarily on the strength of the forces acting on the beam, which depends primarily on the proximity of the walls to the beam. In most accelerators the disposition of the vacuum tank is such as to cause the axial mode to become unstable at lower intensities than would cause the radial mode to become unstable.

The time dependence of the electromagnetic fields excited by the beam may be such as to cause a relation to exist between the phase of the coherent oscillation of different bunches in the beam. Any such relationship of betatron oscillation phases can be said to describe a mode of oscillation of the complete beam. In general there will be as many such modes as there are bunches in the machine. Modes have been observed in accelerators which correspond to a simple phase relationship between bunches. Mixtures of modes have been observed such that there is an apparently random relationship between the betatron oscillation phases of the different bunches. In general a system which will control and damp these oscillations must be able to damp all the different possible modes.

Modes have been observed at very high frequency of wave length shorter than the bunch structure in the accelerator. Systems which control these modes are of the same character as those which control the previously described modes; the requirement for tracking precision, however, is greater.

Therefore, the main object of the present invention is to provide a method of and apparatus for damping coherent betatron oscillations.

Another object of the present invention is to provide a self-adaptive system for damping coherent betatron oscillations.

A still further object of the present invention is to provide a method of and apparatus for damping coherent betatron oscillations wherein the time base for applying the restoring force is derived from the instantaneous frequency of the RF energy source.

A still further object of the invention is to provide a method of and apparatus for damping coherent betatron oscillations wherein the bunches of orbiting charged particles are tracked as they are accelerated about the machine, and a restoring force, proportional to the axial displacement of a given orbiting bunch from a predetermined orbit, is applied to that same displaced bunch.

Briefly, the above objects are accomplished by sensing the displacement of an orbiting particle bunch from a predetermined desirable axial orbit, tracking the displaced bunch in its orbit about the accelerator to distinguish the displaced bunch from other orbiting bunches, applying a restoring force to the displaced bunch at a driving location an odd number of quarter wave lengths of betatron oscillation downstream from the sensing location at the exact time when the displaced bunch passes the driving location. The tracking and timing are accomplished by providing for a discretely variable delay line which receives the displacement signal and delays it for the amount 'of time it takes the bunch to travel from the sensing location to the driving location. The total delay of the delay line is determined by the instantaneous frequency of the RF energy source so that as the angular velocity of the bunch increases responsive to the increase in instantaneous frequency of the RF energy source, the delay line is automatically adjusted in discrete increments to provide precise timing information for the restoring force.

Other objects of the present invention will become apparent from the following detailed disclosure accompanied by the attached drawing in which:

FIG. 1 is a schematic diagram of those elements of the Argonne zero gradient synchrotron particle accelerator necessary to illustrate the present invention;

FIG. 2 is a schematic illustration of a particular mode of betatron oscillation of one bunch of orbiting charged particles;

FIG. 3 is a graph of the axial tune ratio of the accelerator of FIG. 1 as a function of the radial position of the center of the orbiting beam;

FIG. 4 is a block schematic drawing of a complete system according to the principle of the present invention;

FIG. 5 is a circuit diagram illustrating the switching of the master delay lines of FIG. 4;

FIG. 6 is a simplified circuit schematic of a phase detector used in the present invention;

FIG. 7 is a phasor diagram of the input signals of the phase detector of FIG. 6.

Although the present invention is capable of being adapted to any synchrotron particle accelerator, for purposes of illustration it is best understood in terms of a particular particle accelerator. Therefore, the invention will be illustrated within the context of the zero gradient synchrotron (ZGS) particle accelerator located at Argonne National Laboratory, Argonne, Ill.

Referring then to FIG. 1, eight magnet sections 10 are symmetrically placed around a circular path defining the orbit of a plurality of bunches of charged particles being accelerated. Each magnet is provided with a chamber (not shown) running along its axis through which the beam passes. A source of charged particles 12 injects a stream of these particles into orbit at location A for a suitable period of time. This stream of particles immediately upon injection and on successive turns in orbit passes through an RF cavity 14 energized by an RF energy source 15. The portion of this entering and orbiting stream which arrives at the RF cavity at a suitable phase for acceleration undergoes an incremental increase in energy due to the electric field in the cavity. Those arriving at other phases are lost to the chamber walls.

In the Argonne ZGS the radio frequency is chosen so as to form the injected and orbiting beam into eight bunches of particles. Since the velocity of the bunches increases with energy the frequency of the RF in the cavity must increase correspondingly. In the case at hand, the frequency of the RF source 15 starts from 4.4 megacycles per second at injection and increases nonlinearly to 14 megacycles per second at the highest energy.

As the charged particles increase in energy, the magnetic field of magnet sections must correspondingly increase in intensity according to a predetermined relationship with the instantaneous frequency of RF energy source to confine the bunches to a predetermined fixed radial orbit.

The field of magnet sections 10 is perpendicular to the plane of the page of FIG. 1. The illustrated embodiment relates to instabilities involving bunch motions parallel to the magnetic field, consequently perpendicular to the plane of the page of FIG. 1.

One mode of betatron oscillation is illustrated in FIG. 2. The solid sinusoidal line 16 represents the axial location of the center of an orbiting particle bunch, and the dotted portion of the line indicates the path of the center of the orbiting bunch after a proper restoring force has been applied at D. The predetermined desirable orbit for the center is shown as a horizontal straight line 18. In other words, it is desirable that there be no transverse motion of the bunch. This is because such motion may cause beam particles to strike the Wall and be lost from acceleration.

The location indicated by reference letter S of FIG. 2 is shown at its corresponding location in FIG. 1 and represents the angular location at which a pair of induction electrodes, described in more detail below, is placed for sensing axial deviation of the orbiting particle bunch. Reference letter D indicates the angular location of a similar pair of electrodes for driving the beam back to its desired axial position. It is to be noted that betatron oscillations, as indicated in FIG. 2, are unstable as the bunch increases in energy (that is, the amplitude of the oscillation increases), and the beam will eventually strike the top or bottom of the chamber thereby causing a loss of some of the charged particles unless some corrective action is taken.

The tune (axial or radial) of a synchrotron is defined as the ratio of the frequency of betatron oscillation to the angular frequency of an orbiting bunch of charged particles. Therefore, the axial tune of a synchrotron indicates the number of axial betatron oscillations per revolution of a bunch of charged particles about the machine. The tune of an accelerator is determined by the physical parameters of the magnets.

FIG. 3 illustrates the axial tune of the Argonne ZGS as a function of the radial position of the bunch. The tune varies from 0.8 to 0.7 with a median of 0.75 as the beam moves radially from 5 inches inside its center line to 5 inches outside its center line.

As shown in FIG. 2, the center of the orbiting particle bunch goes through approximately three quarters of an oscillation between the time it first passes the location S and its next pass of location S. The present invention is designed to sense a displacement of the center of an orbiting particle bunch from its predetermined desirable position at a sensing location 5, and after tracking that bunch around the accelerator, apply a restoring force proportional to its displacement at a location D, downstream. It is necessary that the restoring force be applied to that bunch of orbiting particles for which a displacement has been sensed, and since there are a plurality of orbiting bunches, tracking is necessary. Further, the restoring force must be of the proper polarity and must be applied at approximately an odd number of quarter wave lengths of axial tune of the unstable oscillation. For the illustrated machine, in which the median axial tune is 0.75, the electrodes excited by the restoring force may be placed at one third of a revolution downstream from the sensing electrodes, or at a full revolution downstream from the sensing electrode, or at one and two thirds revolutions downstream from the sensing electrode, and so on. In the illustrated embodiment, the forcing electrodes are placed at approximately one revolution downstream from the sensing electrodes. They are shown in FIG. 1 and FIG. 2 at D. This requirement of placing the forcing electrodes at an odd number of quarter wave lengths of the axial tune of the accelerator is not critical. A sufficient restoring force can be exerted upon an orbiting particle bunch with relatively loose tolerances with respect to this requirement.

Some restoring force will be applied if a displacement is sensed even if the oscillation is not a peak while the bunch passes the sensing location, as is shown in FIG. 2. Further, it will be noted that once an unstable axial oscillation exists, it cannot escape detection since the sensing electrodes are fixed and the modes of the instability will themselves propagate about the orbit.

In order that all unstable modes be clamped by the system it is necessary that the transit time of the informa tion from the sensing electrodes to the forcing electrodes be equal to the transit time of particles between these two points. When this requirement has been met, coherent betatron oscillations will be damped with a rate 5, where F is the time for oscillations to decrease by a factor of e (the base of natural logarithms) where trrr V: particle velocity u=the tune previously defined AP/Z=the gain of the system, i.e. the transverse momentum kick given when a displacement Z is detected P=the longitudinal momentum of the particles, and

gl il'l6 charge in phase of betatron oscilations experienced by particles in traveling from the pickup electrode to drive electrode electrodes. The desired delay T in the slave delay is given by where R is the number of revolutions traversed by a bunch of orbiting charged particles in passing from the sensing electrodes to the forcing electrodes, and f is the instantaneous orbital revolution frequency of a given bunch of particles. We now choose a unit of time delay 1- The tracking system will continually adjust the length of the slave delay in units of To. Thus, To determines the precision of tracking. We can define a number A which is the ratio of the total delay T to the incremental delay To Ts/T m Let T be the delay in the master delay. The length of master delay cable is chosen to obtain a convenient signal to operate a time detector. Let us require that there be P wave lengths of master oscillator frequency in the cable length of the master delay cable. Since the master oscillator frequency is h (the number of orbiting bunches) times the orbital revolution frequency f,

T =P/hf (4) Now let us choose an incremental change of master delay T1. Then we can define a number A as the ratio of T to 7'1.

1 f' l The function of the time detection circuitry will be to keep the length of the master cable P wave lengths of master oscillator frequency by changing the length of the master delay cable in units of T1. Thus, we have a number A describing the length of the master delay and a number A describing the length of the slave cable. We now set This determines the relationship between the units of cable length 7- and T If this ratio of cable of delay unit is chosen and the cable delays are characterized by A=A then the time detection system which maintains the master delay P wave lengths of master oscillator frequency will automatically maintain the slave cable to the required delay.

In the present case h equals 8. A choice for the pa rameter R in the neighborhood of R=1 is convenient because it provides desirable elapsed betatron phase #1 of Equation 1 and conveniently locates all the circuitry in one straight section of the accelerator. The value of P was chosen to be 7% so as to obtain a quadrature signal as required by the time delay detection method described in detail below. The ratio of 1- to To for the equipment in the ZGS was 0.98. The incremental unit of slave cable 7'0 was chosen to be 6.0 us. In this case the information is returned to the same bunch with a precision of 13.0 ns., well Within the width of a bunch.

It is to be noticed that the orbital revolution frequency of a particle bunch (i.e. one-eighth the frequnecy of the RF energy source) in the ZGS varies from .55 megacycles at injection to 1.75 megacycles at full energy. Therefore the range of A is from 303 to 95. The difference in the values of A is less than 256:2. so that the variable part of A can be synthesized with 8 binary units. The operation of the delay detector is thus to detect a variation in delay in the master cable corresponding to a 3 nanosecond delay in the slave delay and as a consequence of this to subtract or add one unit to the binary number representing the variable part of A. During the normal course of acceleration the time delay detector repeatedly subtracts one unit from A.

In the following description reference will be made to various individual circuits and it is to be noted that all of these are of conventional construction and within the knowledge and skill or a logical extension of the electronic art, The method of time detection, however, is not an obvious extension of the electronic art; and it is described in detail below, and considered an important feature of the present invention.

Referring now to FIG. 4, sensing electrodes 20a and 20b, each having a rectangular U shape, are dimensioned to fit the chamber of the accelerator with a slight spacing parallel to the top of the chamber providing for electrical isolation between electrodes Zita and 26b. Normally the beam passes perpendicular to the plane of the U without touching either electrodes Zita or 2012. Electrode 20a is connected to the input of a conventional cathode follower 21a. Electrode 20b is connected to the input of cathode follower 21b which is identical to cathode follower 21a. The outputs of cathode followers 21a and 21!) are connected to the balanced inputs of a differentiai transformer 22. The output of differential transformer 22, which is a signal representative of the difference in potential presented at its input terminals and hence the difference in potential of electrodes Zita and 20b, is connected to the input of slave delay lines 23, which will be discussed in more detal below. Manual delay 24, which may be an ordinary transmission line, receives the output of slave delay lines 23 and feeds the input of a linear amplifier 25. The output of the linear amplifier 25 drives the forcing electrode 26. The series combination of cathode followers 21a and 21b, differential transformer 22, slave delay lines 23, manual delay 24, and amplifier 25 will hereinafter be referred to as the slave delay loop. The forcing electrode 26 is placed approximately 355.78 around the orbit in the direction of travel of the particles, that is, not quite three-quarters of a wave length of a betatron oscillation downstream from the sensing electrodes 20a and 23b.

In the Argonne ZGS the time base for the application of RF energy, as well as the time base for increasing the intensity of the magnetic field of the accelerator, is derived from a master oscillator 30, which is programmed to have an instantaneous frequency which is a function of time as the orbiting particle bunches are being accelerated. However, it is noted here that the invention may be adapted for use with phase-locked systems where in the orbiting beam provides prime frequency information to the RF power source.

In the illustrated embodiment, the output signal of master oscillator 30 is fed to the input of a low-pass filter 31. The half-power frequency of the low-pass RC filter is well below the range of frequencies of the output signal of the master oscillator 30 and the output of the filter 31 is a signal which is inversely proportional to the frequency of the input signal for constant amplitude input signal to the filter 31. The output of the low-pass filter 31 is connected to the input of a linear broadband amplifier 32. The output of amplifier 32 is connected to the single-ended input of a differential transformer 33. One side of the balanced output of the differential transformer 33 is connected to the input of master delay lines 27 and to input A of a phase detector 34. The other side of the balanced output of differential transformer 33 is connected to input B of the phase detector 34.

The output of the master delay lines 27 is connected to fixed delay lines 23 which may be an ordinary transmission line. The output of the fixed delay line 28 is connected to the input of manual delay lines 29, which also may be ordinary transmission line. The series circuit of the master delay lines 27, the fixed delay line 28, and the manual delay lines 29 provides the total electrical delay of the master delay cable and is hereinafter referred to as the master delay loop. The output of the manual delay lines 29 is connected to point C of the phase detector 34. The phase detector 34 is described below along with the operation of the entire time delay detector shown enclosed by the dashed line in FIG. 4 and which consists of low-pass filter 31, broadband amplifier 32, differential transformer 33, phase detector 34, summing amplifier 35, and level detectors 36a and 36b. The outputs of the phase detector 34 are connected to the inputs of a summing amplifier 35. The output of the summing amplifier 35 is connected to the inputs of a forward level detector 36a and a backward level detector 36b. The output of the forward level detector 36a is connected to the count up input of an up-down binary counter 37, The output of the backward level detector 36b is connected to the count down input of the up-down binary counter 37. The binary outputs of the binary counter 37 are connected to the slave delay lines 23 and the master delay lines 27 such that each binary digit of the counter 37 drives a corresponding RF switch unit in the slave and master delay lines in parallel. The RF switch units in the master and slave delay lines are described in more detail below.

FIG. shows a simplified diagram of the method used to switch eight individual cables comprising slave delay lines 23. The same circuit and principle are used in the design of master delay lines 27, but only the former is illustrated here. As previously indicated, the individual cables comprising the slave delay lines 23 have lengths starting with 70 6.0 nanoseconds and increase thereafter by a factor of two so that the longest is 6.() 2 or 768 nanoseconds. Each individual cable is switched into or out of the circuit responsive to the output signal of counter 37 such that when the jth digit of the binary counter is in the on state, then the cable of length (60x2 nanoseconds length is inserted in the series circuit of cables. Thus 2 =256 series cable circuit combinations exist with adjacent number connections being 6.0 nanoseconds apart and a total range of delay from 0 to 1536 nanoseconds.

The RF switch units, illustrated by the mechanical switch notation in FIG. 5, are of conventional PN junction diode switch design.

The operation of the time delay detector is described below. Referring to FIG. 6, a resistor 50 provides termination load for the master delay loop. A resistor 51 provides a termination load for the output of the balanced differential transformer 33. A capacitor 53 charges up to the peak value of the signal between points A and C through a diode 55 and thus, the DC. voltage on capacitor 53 represents the magnitude of the phasor CA. Similarly, a capacitor 52 charges up to the peak value of the signal between points B and C through a diode 54 and thus, the DC. voltage on capacitor 52 represents the magnitude of the phasor CB. A resistor 56 provides a slow discharge path for capacitors 52 and 53 so that the DC. voltages on capacitors 52 and 53 may change with time sufiiciently fast for operation of the system. The sum of the voltages at points D and E of FIG. 6 represents the difference in magnitudes of phasors CB and CA shown in FIG. 7.

The following derivation shows that, for a fixed amplitude with frequency signal out of the master oscillator 30, the voltage out of the summing amplifier 35 is a nearly linear function of the error in time delay of the master delay loop. For a constant amplitude signal at the input of the low-pass filter 31, the amplitudes of phasors A and B are equal and given by f where K =a constant, a value of which depends upon the gain characteristic of the broadband amplifier 32 and the attenuation characteristics of the low-pass filter 31 and the broadband transformer 33 f=instantaneous frequency of the master oscillator delay cable is in phase error by an amount 5. It should be noted that the magnitude of C is related to the magnitude of A by the amount of attenuation in the master delay cable. By using high attenuation cable in the fixed delay line 28 and manual delay line 29 and low attenuation cable in the master delay lines 27, the attenuation of the signal in passing through the master delay loop is nearly constant and may be defined as I Z=Q I Referring to the phasor diagram of FIG. 7, let

t 1 1. c= 1 x 6=C /1r/25=C[sin 5+j cos a (10) From Equation 8, A=K /f and since sin 6&6 for 6 small,

then M becomes 1K K 5 Al 2 The value of M given by Equation 16 represents the error in time delay (within a constant factor) of the master delay loop. The output of the summing amplifier 35 is therefore a linear function of the time delay error.

The reference voltages of the forward level detector 36a and the backward level detector 361) are set to cause a count signal to proceed to the counter 37 when the time delay error signal corresponds to a time delay error of 13.0 nanoseconds. This causes the counter 37 to advance or regress (add or subtract an integer from the value of A as previously described), depending upon the sense of the time error signal, and thus, cause an adjustment of the slave and master delay lines 27 and 23 to within the $3.0 nanosecond acceptable range.

Although our invention has been described in a specific embodiment, various modifications and equivalent structures may be substituted without deviating from the principle thereof, and we, therefore, do not intend to limit the 9 scope of our invention thereby, but wish it to be determined only by the spirit and scope of the appended claims.

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. In a synchrotron particle accelerator having a source of increasing-frequency RF energy for accelerating bunches of charged particles in a fixed, closed orbit defined by a magnetic field increasing in intensity as the frequency of said RF energy source increases, the instantaneous frequency of revolution of said bunches being a number, 7, apparatus for damping betatron oscillations of said orbiting bunches comprising:

means associated with a sensing location of said orbit for generating a displacement signal representative of the axial displacement of an orbiting bunch from a predetermined desirable orbit:

forcing means located at a driving location of said orbit a total number, R, of orbital revolutions downstream from said sensing location, R being approximately an odd number of quarter wave lengths of said betatron oscillations;

discretely variable slave delay means receiving said displacement signal for delaying said displacement signal; discretely variable master delay means receiving the output signal of said RF energy source for delaying said signal for a time, T =P/hf, where P is the number of wavelengths of said RF energy source signal in the master delay :and h is the number of bunches in the accelerator, whereby the total delay time, T of said master delay means is related to the time, T required for said displacement signal to propagate from said sensing location to said forcing location by the expression T /T =P/Rh;

detector means receiving said RF energy source output signal and the output signal of said master delay means for detecting deviations from a quadrature phase relationship between said source signal and said delayed signal and for generating an error signal representative of said deviation;

means responsive to said error signal for varying said master delay means in discrete increments to reduce said error signal, and for varying the delay of said slave delay means in discrete increments to be related to the delay time, T of said master delay by the relationship T /T =P/Rh, thereby adjusting the propagation time of said displacement signal from said sensing location to said forcing location to be related to the total delay time T of master delay means by the said relationship;

means receiving said delayed displacement signal for generating a forcing signal proportional to said displacement signal and for applying said forcing signal to said forcing means thereby correcting deviation of said displaced bunch from said predeter' mined desirable orbit.

2. The apparatus of claim 1 wherein said detector means comprises:

a difference means receiving the signal of said RF energy source for generating first and second signals respectively in phase with and in phase opposition to said RF energy source signal;

a phase detector circuit receiving the signal delayed through said master delay loop and the signals generated by means for detecting the amplitude of a first phasor representing the instantaneous voltage difference between said master delayed signal and said first difference means signal and the amplitude of a second phasor representing the instantaneous voltage difference between said second difference means signal and said master delayed signal;

summing means receiving said first and second phasor signals for summing the amplitudes of said first and second phasor signals, thereby generating said aforementioned error signal representative of the time delay error of said master delay means.

3. The apparatus of claim 1 wherein said means for varying said master delay means and said slave delay means comprises:

a first discriminator means receiving said error signal for generating an output signal in response to the signal of said summing means exceeding a predetermined threshold representative of a maximum desirable error signal;

a second discriminator means receiving said error sig nal for generating an output signal in response to the signal of said summing means falling below a predetermined threshold representative of a minimum desirable error signal;

counter means receiving the output signals of said first and second discriminator means for increasing a binary count responsive to the output signal of said first discriminator and for decreasing said binary count responsive to the output signal of said second discriminator means;

a first set of discrete delay lines, one for each significant binary digit of said counter, each succeeding delay line increasing in length by a factor of two, adapted to be connected in circuit with said master delay means;

a second set of discrete delay lines adapted to be connected in circuit with said slave delay means;

switching means associated with each of said first and second sets of said delay lines for switching individual delay lines in and out of their respective circuits in response to the binary count of said counter such that the total lengths of said master delay means and said slave delay means are related by expression T T =P/Rh.

References Cited UNITED STATES PATENTS 3,089,092 5/1963 Plotkins 328-235 X 3,263,136 7/1966 Gordon 328--235 X 3,328,708 6/1967 Smith et al 328-235 JAMES W. LAWRENCE, Primary Examiner. C. R. CAMPBELL, Assistant Examiner. 

1. IN A SYNCHROTRON PARTICLE ACCELERATOR HAVING A SOURCE OF INCREASING-FREQUENCY RF ENERGY FOR ACCELERATING BUNCHES OF CHARGED PARTICLES IN A FIXED, CLOSED ORBIT DEFINED BY A MAGNETIC FIELD INCREASING IN INTENSITY AS THE FREQUENCY OF SAID RF ENERGY SOURCE INCREASES, THE INSTANTANEOUS FREQUENCY OF REVOLUTION OF SAID BUNCHES BEING A NUMBER, F, APPARATUS FOR DAMPING BETATRON OSCILLATIONS OF SAID ORBITING BUNCHES COMPRISING: MEANS ASSOCIATED WITH A SENSING LOCATION OF SAID ORBIT FOR GENERATING A DISPLACEMENT SIGNAL REPRESENTATIVE OF THE AXIAL DISPLACEMENT OF AN ORBITING BUNCH FROM A PREDETERMINED DESIRABLE ORBIT; FORCING MEANS LOCATED AT A DRIVING LOCATION OF SAID ORBIT A TOTAL NUMBER, R, OF ORBITAL REVOLUTIONS DOWNSTREAM FROM SAID SENSING LOCATION, R BEING APPROXIMATELY AN ODD NUMBER OF QUARTER WAVE LENGTHS OF SAID BETATRON OSCILLATIONS; DISCRETELY VARIABLE SLAVE DELAY MEANS RECEIVING SAID DISPLACEMENT SIGNAL FOR DELAYING SAID DISPLACEMENT SIGNAL; DISCRETELY VARIABLE MASTER DELAY MEANS RECEIVING THE OUTPUT SIGNAL OF SAID RF ENERGY SOURCE FOR DELAYING SAID SIGNAL FOR A TIME, TM=P/HF, WHERE P IS THE NUMBER OF WAVELENGTHS OF SAID RF ENERGY SOURCE SIGNAL IN THE MASTER DELAY AND H IS THE NUMBER OF BUNCHES IN THE ACCELERATOR, WHEREBY THE TOTAL DELAY TIME, TM, OF SAID MASTER DELAY MEANS IS RELATED TO THE TIME, TS, REQUIRED FOR SAID DISPLACEMENT SIGNAL TO PROPAGATE FROM SAID SENSING LOCATION TO SAID FORCING LOCATION BY THE EXPRESSION TM/TS=P/RH; DETECTOR MEANS RECEIVING SAID RF ENERGY SOURCE OUTPUT SIGNAL AND THE OUTPUT SIGNAL OF SAID MASTER DELAY MEANS FOR DETECTING DEVIATIONS FROM A QUADRATURE PHASE RELATIONSHIP BETWEEN SAID SOURCE SIGNAL AND SAID DELAYED SIGNAL AND FOR GENERATING AN ERROR SIGNAL REPRESENTATIVE OF SAID DEVIATION; MEANS RESPONSIVE TO SAID ERROR SIGNAL FOR VARYING SAID MASTER DELAY MEANS IN DISCRETE INCREMENTS TO REDUCE SAID ERROR SIGNAL, AND FOR VARYING THE DELAY OF SAID SLAVE DELAY MEANS IN DISCRETE INCREMENTS TO BE RELATED TO THE DELAY TIME, TM, OF SAID MASTER DELAY BY THE RELATIONSHIP TM/TS=P/RH, THEREBY ADJUSTING THE PROPAGATION TIME OF SAID DISPLACEMENT SIGNAL FROM SAID SENSING LOCATION TO SAID FORCING LOCATION TO BE RELATED TO THE TOTAL DELAY TIME TM OF MASTER DELAY MEANS BY THE SAID RELATIONSHIP; MEANS RECEIVING SAID DELAYED DISPLACEMENT SIGNAL FOR GENERATING A FORCING SIGNAL PROPORTIONAL TO SAID DISPLACEMENT SIGNAL AND FOR APPLYING SAID FORCING SIGNAL TO SAID FORCING MEANS THEREBY CORRECTING DEVIATION OF SAID DISPLACED BUNCH FROM SAID PREDETERMINED DESIRABLE ORBIT. 